Optical sensor interrogation techniques now form a mature field of research where computational techniques are often used to improve the process of monitoring optical sensors. Optical sensors are usually subject to uniform fields of certain types of perturbation such as temperature or strain. In one use, the spectrum of the light reflected by a sensor has its peak monitored, indicating the magnitude of the perturbation. Finding the peak of sample points is a well used method to reduce the noise on the returned peak centre value. For example, FIG. 1 shows a sequence of ‘sampling points’ captured by a measuring device, such as a sensor. It is desirable to measure the ‘centre’ of a ‘peak’ in ‘sample points’ accurately in a computationally efficient manner.
Fitting sampling points in order to accurately ascertain a centre wavelength/frequency has been shown to provide a high level of accuracy. Depending on the fitting approach taken (Gaussian, Polynomial etc.) it can be challenging to perform a large number of computationally demanding accurate fits in a timely and efficient manner.
A Gaussian fit has been shown to provide accurate centres but the Gaussian function is non-linear with respect to its fitting parameters and therefore requires an iterative algorithm such as the Levenberg-Marquardt algorithm to perform the minimization of its sum of squares required for a least squares fit. These non-linear minimization algorithms are computationally intensive, require significant resources when implemented in hardware and their iterative nature leads to non-deterministic runtimes making them less suitable to real-time systems. A polynomial is a linear function with respect to its fitting parameters and therefore a polynomial fit can be solved in constant time by solving a set of linear equations. The higher the polynomial order the better the fit, however the higher order also introduces more degrees of freedom and this leads to a high level of instability and greater noise in the calculated centre wavelength/frequency values.
A paper publication by Rivera E et al and entitled ‘Accurate strain measurements with Fiber Bragg sensors and wavelength references’, Smart Materials and Structures, IOP publishing Ltd, Bristol GB, col. 15, no. 2, April 2006 discloses an accurate strain measurement using fiber Bragg sensors and wavelength measurements. Rivera et al. discloses a polynomial fit which provides moderate accuracy, when compared to Lorentzian and Gaussian described above. A second order polynomial, at minimum, is required to fit an FBG and using this does not constrain the peak to be symmetrical, but FBG profiles are largely symmetrical. Gaussian and Lorentzian profiles are symmetrical and using these in FBG fits imposes an assumption of symmetry, essentially providing a matched filter which is more resilient to noise than the polynomial approach. Rivera et al discloses that the polynomial fit is more computationally efficient than the lower noise approaches investigated, namely Gaussian and Lorentzian, however noise becomes a problem for high sensitivity operation. Systems which have a high sensor count combined with a requirement for high sensitivity and high frequency operation require a combination of high computational efficiency and effective noise tolerance. Thus Rivera does not offer a solution for high-frequency, high-sensor-count, high-sensitivity optical sensing.
It is therefore an object to provide an improved system and method to measure a centre wavelength/frequency accurately in an optical system at high frequency and high sensitivity.